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**HallsofIvy** Are you referring to

$\displaystyle V_{\text{out}}= \frac{R_2}{R_1+ R_2}V_{\text{in}}$?

Multiply both sides by $\displaystyle R_1+ R_2$ to get

$\displaystyle V_{\text{out}}(R_1+ R_1)= V_{\text{out}}R_1+ V_{\text{out}}R_2= R_2V_{\text{in}}$

Now, get those 2 terms including [tex]R_2[tex] alone on one side by subtracting $\displaystyle R_2V_{\text{in}}$ and $\displaystyle V_{\text{out}}R_1$ from both sides:

$\displaystyle V_{\text{out}}R_2- R_2\V_{\text{in}}= R_2(V_{\text{out}}- V_{\text{in}})= -V_{\text{out}}R_1$

Finally divide both sides by $\displaystyle V_{\text{out}}- V_{\text{in}}$

$\displaystyle R_2= \frac{-V_{\text{out}}}{V_{\text{out}}- V_{\text{in}}}R_1= \frac{V_{\text{out}}}{V_{\text{in}}- V_{\text{out}}}R_1$.